Formula used
The fiber nonlinear coefficient (gamma) is commonly modeled as:
- n₂: nonlinear refractive index (Kerr coefficient).
- λ: optical wavelength.
- Aeff: effective mode area.
If you pick “Estimate Aeff from MFD”, the calculator uses Aeff ≈ π(MFD/2)² as a practical approximation.
How to use this calculator
- Select whether you know Aeff directly or want to estimate it from MFD.
- Enter n₂ with the correct unit, then enter the wavelength λ.
- Provide Aeff or MFD, depending on your chosen method.
- Pick your preferred output unit and press Compute Gamma.
- Use the CSV or PDF buttons to export the latest result.
Example data table
| Case | n₂ (m²/W) | λ (nm) | Aeff (µm²) | γ (1/(W·km)) |
|---|---|---|---|---|
| Single‑mode silica | 2.6e‑20 | 1550 | 80 | ~1.32 |
| Smaller mode area | 2.6e‑20 | 1550 | 50 | ~2.11 |
| Shorter wavelength | 2.6e‑20 | 1310 | 80 | ~1.56 |
Article
1) What the nonlinear coefficient γ represents
The nonlinear coefficient γ links optical power to Kerr nonlinearity inside a guided mode. A practical approximation is the nonlinear phase shift φNL ≈ γ·P·L. Higher γ means stronger nonlinear behavior at lower power or shorter length.
2) Interpreting the material parameter n2
The parameter n2 is the Kerr coefficient describing how refractive index changes with optical intensity. Silica near 1550 nm is often around 2.6×10−20 m2/W, but values vary by material and fabrication. Because γ scales linearly with n2, trustworthy data is important.
3) Why effective area Aeff strongly controls γ
Effective area Aeff captures how concentrated the mode is. For the same launched power, smaller Aeff produces higher intensity, increasing nonlinear interaction strength and raising γ. If you only know mode field diameter, a useful starting estimate is Aeff ≈ π(MFD/2)2.
4) Wavelength dependence and unit consistency
For fixed n2 and Aeff, the formula gives γ ∝ 1/λ, so shorter wavelengths produce larger γ. Most errors in practice come from unit mismatch, especially λ in nanometers and Aeff in square micrometers. Converting to meters and m2 keeps the calculation consistent.
5) Typical magnitude checks for fiber work
As a quick check, a common single-mode silica fiber can yield about 1 to 2 1/(W·km) near 1550 nm when Aeff is roughly 80 µm2. Halving Aeff roughly doubles γ. Moving from 1550 nm to 1310 nm raises γ by about 18% if other parameters stay similar.
6) Design implications in links and nonlinear optics
γ feeds directly into models of self-phase modulation, cross-phase modulation, and four-wave mixing. In communication links, larger γ can increase nonlinear penalties and interacts with dispersion and loss. In nonlinear experiments, larger γ improves efficiency for spectral broadening and parametric interactions at a given power.
7) Practical input sourcing and measurement notes
Aeff is mode dependent and can change with wavelength, bending, and index profile. Datasheets or mode solvers provide the best Aeff values for an operating band. MFD-based estimates are useful for early comparisons, but confirm with measured or modeled Aeff for final design decisions.
8) A reliable workflow using this calculator
Select whether you will enter Aeff directly or estimate it from MFD, then enter n2 and λ with units. Review both outputs (1/(W·m) and 1/(W·km)) and compare against typical ranges. If results are off by orders of magnitude, recheck units and scientific notation.
FAQs
1) What unit should I use for n2?
Use m2/W when possible. If your source lists cm2/W, select that unit and the calculator converts it to m2/W automatically.
2) Is Aeff the same as core area?
No. Aeff is a mode property based on the field distribution. It can be larger than the physical core area and varies with wavelength and waveguide profile.
3) How accurate is the MFD-based Aeff estimate?
It is a practical approximation for quick comparisons in many single-mode cases. For specialty fibers or precise modeling, use Aeff from a mode solver or manufacturer data.
4) Why does γ drop when wavelength increases?
The standard formula includes 1/λ. With n2 and Aeff fixed, longer wavelengths reduce γ, lowering nonlinear phase shift per watt per meter.
5) Should I output 1/(W·m) or 1/(W·km)?
Both are valid. 1/(W·km) is common in fiber specifications, while 1/(W·m) is convenient for short integrated devices. This tool provides both for cross-checking.
6) What causes unrealistically large γ values?
The usual causes are unit mistakes: λ entered in nm but treated as meters, or Aeff entered in µm2 but treated as m2. Recheck units and exponent notation.
7) Does this calculator include dispersion or loss effects?
No. It computes the material-and-geometry nonlinear coefficient γ from n2, λ, and Aeff. Dispersion and loss are separate parameters used in propagation models.